Latent Noise Injection for Private and Statistically Aligned Synthetic Data Generation

TL;DR

This paper introduces Latent Noise Injection with Masked Autoregressive Flows to generate privacy-preserving synthetic data that closely matches the true distribution, especially in high-dimensional settings, while enabling reliable statistical inference.

Contribution

It proposes a novel latent space perturbation method that improves convergence and privacy guarantees in synthetic data generation using flow models.

Findings

Achieves local differential privacy with a single perturbation parameter.

Restores classical efficiency through meta-analysis aggregation.

Demonstrates robustness against membership inference attacks.

Abstract

Synthetic Data Generation has become essential for scalable, privacy-preserving statistical analysis. While standard approaches based on generative models, such as Normalizing Flows, have been widely used, they often suffer from slow convergence in high-dimensional settings, frequently converging more slowly than the canonical $1/\sqrt{n}$ rate when approximating the true data distribution. To overcome these limitations, we propose a Latent Noise Injection method using Masked Autoregressive Flows (MAF). Instead of directly sampling from the trained model, our method perturbs each data point in the latent space and maps it back to the data domain. This construction preserves a one to one correspondence between observed and synthetic data, enabling synthetic outputs that closely reflect the underlying distribution, particularly in challenging high-dimensional regimes where traditional sampling struggles. Our procedure satisfies local $(\epsilon, \delta)$-differential privacy and introduces a single perturbation parameter to control the privacy-utility trade-off. Although estimators based on individual synthetic datasets may converge slowly, we show both theoretically and empirically that aggregating across $K$ studies in a meta analysis framework restores classical efficiency and yields consistent, reliable inference. We demonstrate that with a well-calibrated perturbation parameter, Latent Noise Injection achieves strong statistical alignment with the original data and robustness against membership inference attacks. These results position our method as a compelling alternative to conventional flow-based sampling for synthetic data sharing in decentralized and privacy-sensitive domains, such as biomedical research.